Parametric T-Spline Face Morphable Model for Detailed Fitting in Shape Subspace

Pre-learnt subspace methods, e.g., 3DMMs, are significant exploration for the synthesis of 3D faces by assuming that faces are in a linear class. However, the human face is in a nonlinear manifold, and a new test are always not in the pre-learnt subspace accurately because of the disparity brought by ethnicity, age, gender, etc. In the paper, we propose a parametric T-spline morphable model (T-splineMM) for 3D face representation, which has great advantages of fitting data from an unknown source accurately. In the model, we describe a face by C^2 T-spline surface, and divide the face surface into several shape units (SUs), according to facial action coding system (FACS), on T-mesh instead of on the surface directly. A fitting algorithm is proposed to optimize coefficients of T-spline control point components along pre-learnt identity and expression subspaces, as well as to optimize the details in refinement progress. As any pre-learnt subspace is not complete to handle the variety and details of faces and expressions, it covers a limited span of morphing. SUs division and detail refinement make the model fitting the facial muscle deformation in a larger span of morphing subspace. We conduct experiments on face scan data, kinect data as well as the space-time data to test the performance of detail fitting, robustness to missing data and noise, and to demonstrate the effectiveness of our model. Convincing results are illustrated to demonstrate the effectiveness of our model compared with the popular methods.